0071549226 ar007

7.1 GRAIN SIZES AND ORDERS OF MAGNITUDE

7.1.1 Size Ranges or Grades

The individual particles that make up a soil vary in size by orders of magnitude.For example, the size difference between a 0.002mm clay particle and a 2mdiameter boulder is 6 orders of magnitude, or about the same as between aVolkswagen and the Moon. It therefore is convenient to define particle size gradesby defining discrete ranges in particle sizes that define clay, silt, sand, gravel,cobbles, and boulders. Each size grade covers a range in particle sizes––that is, allgravel particles obviously are not the same size. ‘‘Clay’’ thus defined relates to arange in particle sizes without regard to their mineralogy. However, because of arelationship between weatherability of different minerals and particle size, mostclay-size particles are composed of the special group of minerals designated as clayminerals. A particular soil therefore will consist of varying percentages of clay,silt, and sand sizes with occasional coarser material.

7.2 GRADATION CURVES

7.2.1 Logarithmic Grain-Size Scale

Because of the broad range in particle sizes that can make up a particular soil,sizes are conveniently plotted on a logarithmic scale. The advantage becomesapparent by comparing Fig. 7.1, where sizes are plotted on a linear scale, withFig. 7.2, where the size distribution for the same glacial till soil is plottedlogarithmically. Figure 7.2 also shows the huge variations in particle sizes betweensome common soils deposited by wind, water, and ice.

7 Particle Size and Gradation

143

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7.2.2 Particle Size Accumulation Curves

The graphs in Figs. 7.1 and 7.2 show particle size data as ‘‘percent finer’’ thaneach size on a dry-weight basis. This is a particle size accumulation curve.

Figure 7.3 shows the relationship between an accumulation curve and a bar graphor histogram representation of the same data. The data are obtained by passingsoil through a succession of progressively finer sieves and weighing the amountretained on each sieve. The bar heights in the upper graph show each of theseamounts. Mathematically the upper graph is the differential or slope of the lowergraph, which is the particle size distribution curve. Conversely, the lower graphrepresents the integral of the upper graph.

The median or average grain size can be read directly from a particle sizeaccumulation curve, as shown by the arrows in Fig. 7.3. The median grain size isdefined on the basis that 50 percent of a soil by weight is finer, and 50 percent is

Figure 7.1

Plottingparticle sizes to alinear scaleemphasizes thewrong end of thesize scale—thegravel and not theclay.

Figure 7.2

Semilogarithmicgraph of the sameparticle size datafor the glacial tillsoil and forseveral othersoils.

144 Geotechnical Engineering

Particle Size and Gradation


coarser. In Fig. 7.3 this percentage occurs at 0.021mm, which is in the sizerange for silt. The median grain size is designated by D50. Another reference sizethat has been found to relate to the permeability or hydraulic conductivity of soilsis D10.

Example 7.1What is D10 for the soil in Fig. 7.3?

Answer: Slightly smaller than 0.001mm.

7.2.3 Modes

The highest bar on a histogram data plot indicates a dominant particle size, whichis designated the mode. Although a mode is not the same as a median size, inFig. 7.3 the two are close because of the symmetrical shape of the major portionof the histogram. This symmetry reflects a statistical normal distribution, not ofparticle sizes, but of logarithms of the particle sizes because particles settleout of a suspension according to the square of their diameter instead of theirdiameter.

In Fig. 7.3 another mode occurs in the clay size range smaller than 0.002 mm,probably due in part to clay adhering to coarser grains when they settled out. Twoor more modes also can indicate soil mixtures, as when two strata are combined inone sample or sand has infiltrated into interstices in a gravel deposit. B horizonsoils are bimodal because of infiltration by clay from the A horizon. Engineeredsoils often are mixtures in order to improve their engineering properties.

Figure 7.3

Relation between aparticle sizeaccumulationcurve showing amedian grain sizeand a histogramshowing modalsizes.

Particle Size and Gradation 145



While a histogram is instructive, an accumulation curve is easier to plot and isalmost universally used in engineering. Modes occur on an accumulation curvewhere slopes are steepest, and component soil percentages are indicated where thecurve flattens out.

Example 7.2Large samples of glacial till often contain a mix of different component soils. What are

component percentages in the glacial till in Fig. 7.2?

Answer: The first steep section of the curve is at 41%, which therefore represents onecomponent soil. The second break is at 60% so the difference is 60 – 41¼ 19%, which

represents a second component. Similarly, the third break at 90% defines 90 – 60¼ 30% fora third component, and a fourth component makes up the remaining 10%. The threecomponents percentage are 41þ 19þ 30þ 10¼ 100%. The respective soils are (a) mainlyclay plus some silt, (b) all silt, (c) mainly fine sand, and (d) a mixture of coarse sand and

gravel.

7.3 DEFINING SIZE GRADES

7.3.1 Making the Grades

Not all sand particles are exactly the same size, which means that ‘‘sand’’ mustcover a range of particle sizes, the only requirement being that they are smallerthan gravel and larger than silt grains. Natural size boundaries occur betweengravel and sand, between sand and silt, and between silt and clay, but theboundaries are transitional and somewhat arbitrary, and different organizationshave adopted different definitions.

Gravel particles require a higher water velocity to be moved than sand, and winddoes not move them at all. Sand particles move by bouncing, or saltation, and siltgrains are mainly carried in suspension, as the mud in muddy water or the dustin air. Clay particles are so fine that they are very slow to settle out of suspensionand consist of separate mineral species, the clay minerals.

7.3.2 Sieve Sizes

Soils are separated into size grades by sieving, or sifting through a series or ‘‘nest’’of standardized wire mesh sieves arranged from the coarsest down to the finest.Common sieve sizes used in engineering are listed in Table 7.1.

A sieve is a wire fabric, so the sieve number does not describe the size of theopening but designates the number of wires per inch or millimeter. As a matter ofconvenience some size grades are defined on the basis of standard sieve sizes:gravel, for example, commonly designates particles that are coarser than 2mm,which is the size of the opening in a No. 10 (wires to the inch) sieve.




One complication is that sieve openings are not round; they are approximatelysquare. Spherical particles can pass through regardless of their orientation, butfew soil grains are spheres. Sieves therefore are vigorously shaken or vibrated for aprescribed time in a sieve shaker in order to achieve reproducibility of the data.

7.3.3 Details of the Gravel-Sand Size Boundary

Although the most common size boundary between sand-size and gravel-sizeparticles is 2mm, this size separation is not universal, even within geotechnicalengineering.

The Unified Soil Classification System used in earth dam and foundationengineering makes the separation at the No. 4 (3/16 in.) sieve, and materialfrom 4.76 to 2mm in diameter is considered ‘‘very coarse sand.’’ These and othersize boundaries are indicated in Fig. 7.2 Because the boundaries differ, it isimportant that they be defined or included on graphs showing the particle sizedistribution, as indicated by the vertical lines and grade names across the bottomin Fig. 7.2.

7.3.4 The Sand-Silt Size Boundary

As silt particles are fine enough to be carried in suspension they show little or norounding of corners, whereas sand particles typically are abraded and rounded atthe corners and edges from having been transported and bounced along by windor water. However, the boundary is transitional, and for convenience it often isdefined on the basis of a sieve size. In geotechnical engineering practice theboundary between sand and silt usually is that of a 200-mesh sieve opening,0.075mm or 75 mm (micrometers). The earlier designation was ‘‘microns.’’) Sandtherefore presents a range in particle sizes between 0.074 and 2mm diameter,a size ratio of 27.

No. (wires per inch) Opening, mm Comment Table 7.1

Standard sieve sizes

used in geotechnical

engineering

(Lid) ––

4 4.75 Gravel

10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.0 . . . . . . . . . Size separating gravel and sand

20 0.85

40 0.425

�

60 0.25 Sand

140 0.106 #200 . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.075 . . . . . . . . . Size separating

sand from silt

(Pan) –– Silt and clay fall on

through and collect in the pane




Soil scientists prefer to make the separation between sand and silt at 0.020mm or20 mm. However, as shown by the loess and sand soils in Fig. 7.2, the naturalboundary may be closer to the No. 200 sieve (0.074mm) or even slightly larger.Geologists sometimes use 1/16mm¼ 0.067mm, sometimes rounded off to0.06mm. However, the occurrence of a natural break in the general vicinitytends to diminish the influence on constituent percentages.

7.3.5 The Silt-Clay Size Boundary

The most widely accepted size definition of clay is particles that are finer0.002mm or 2 mm. An earlier definition was based on the resolving powerand eyepiece calibration of a light microscope at the U.S. Bureau of Soils,and set the boundary at 0.005mm (5 mm). Later mineralogical investiga-tions showed that this boundary is too high, but meanwhile it became estab-lished and still is occasionally used in geotechnical engineering. The 0.005mmsize also requires less interpolation from measurements that routinely aremade after 1 hour and 1 day testing time. This is discussed in more detail insection 7.4.6.

7.3.6 Silt-Clay Boundary Based on Physical Properties

Another approach is to define clay on the basis of its plasticity or moldability withwater, as silt is crumbly while clay is sticky and can be molded into differentshapes. These relationships are quantified by two simple tests called Atterberglimits. These tests and the relationship to engineering soil classifications arediscussed in Chapter 12. The limits define a moisture content range over which asoil can be molded. This range is the plasticity index, which is a fundamental soilproperty in geotechnical engineering.

In order to avoid possible confusion between the two approaches, a clay contentbased on particle size may be referred to as clay-size material.

7.4 MEASURING PARTICLE SIZES

7.4.1 General Approach to Size Measurement

Some shortcuts are in order because so many particles must be measured in orderto obtain statistical reliability. One shortcut is to use sieves and screen arepresentative soil sample. Another approach that is used for particle sizes toosmall to be separated on sieves is to disperse the soil in water and make adetermination based on the sedimentation rate, with largest particles settling thefastest.

One of the most important steps in analysis is obtaining a representativesoil sample. Large samples are spread out on a flat surface and ‘‘quartered,’’




that is, cut into four pie-shaped sectors and then combining opposing sectorsand returning the other half of the sample to the bag. This procedure isrepeated until the soil sample is small enough to be managed. A more rapidmethod for quartering uses a ‘‘riffle-type’’ sample splitter that has parallelshuts, with half directing the sample one way and the other half the other. Soilsare air-dried prior to quartering and sieving, but as discussed in Chapter 6,if a soil contains halloysite clay mineral, it should be saved and sealed againstdrying.

7.4.2 Sedimentation Analysis

Sieving is appropriate for measuring the amounts of sand and gravel in a soil, butsilt and clay sizes are too small to be separated by sieving. Also, clay particlestend to be aggregated together into coarser particles and to occur as coatingson coarser particles. Gravel is removed by sieving, and the rest of the soilnormally is soaked in water and then agitated and dispersed using a chemicaldispersing agent. The suspension then is tested by measuring sedimentation rates,and finally the part of the soil that is retained on a fine sieve is dried and analyzedby sieving.

The general procedure is as follows. After sieving to remove gravel and coarserparticles, the soil is soaked in water containing a small amount of a chemicaldispersing agent, usually sodium hexametaphosphate, a water softener that isavailable in the detergent department of a supermarket. The dispersing agentforces substitution of sodium ions for exchangeable calcium ions on the clay bycreating an insoluble phosphate precipitate.

The suspension then is agitated for a set amount of time with a standardizedmechanical or air-jet stirring device. Ideally this will separate but not breakindividual soil grains. The soil suspension is diluted to 1 liter in a vertical flask andstirred in preparation for starting the test.

The starting time is noted and the suspension is allowed to settle for various timeintervals. After each time interval, the density of the suspension is determined at aparticular depth with a hydrometer. An alternative method is to sample thesuspension with a pipette, then dry and weigh the sample.

The larger the weight of particles remaining in suspension, the denser the liquid,and the higher the hydrometer will float. An engineering hydrometer is calibratedto read directly in grams of soil per liter of suspension. Readings normally aretaken after 1 minute and at various time intervals to 1 hour and then after24 hours.

After the sedimentation analysis is completed, the soil is washed on a fine sieve toremove the silt and clay particles, then dried and the sand fraction analyzed bypassing through a series of sieves.




7.4.3 Sedimentation and the Percent Finer

A sedimentation analysis automatically measures the amounts finer than a specificgrain size. This is illustrated in Fig. 7.4: after a certain time all particles larger thana certain depth have settled a calculated distance and therefore cannot occur atdepths shallower than that distance. On the other hand, finer particles remainsuspended and therefore are measured.

After each hydrometer reading the hydrometer is removed so that particles willnot settle on the bulb. Removal stirs a small portion of the upper part of thesuspension, but the effect is small so long as particles move horizontally andnot vertically relative to the suspension—as the instrument is removed, the level ofthe suspension goes down, and when it is replaced the level goes back up.The depth to the center of volume of the submerged part of the hydrometeris the effective sampling depth that is used in the calculations, and depends onthe depth of sinking. This depth is obtained from a calibration chart or table,Table 7.2.

Figure 7.4

Sampling theoryin sedimentationanalysis: at aparticularsampling depththe suspensioncontains arepresentativesample of all sizessmaller than thesize that will settleto that depth.




Temperature also must be controlled and measured to enable correction forchanges in the fluid viscosity.

7.4.4 Stokes’ Law of Sedimentation

In 1851 a British mathematician, G.G. Stokes, solved for the settlementvelocity of spherical particles in a suspension by equating their buoyant weightto viscous drag on the outer surfaces. Surface area increases in proportion tothe radius while weight increases as the radius cubed, so the larger the particle,the faster it will settle. The classic derivation for Stokes’ formula in the cgssystem is

R ¼ 6�r�v ð7:1Þ

where R is the resisting force in g cm/s2, r is the particle radius in cm, � is the fluidviscosity in poise or g-cm�1s�1, and v is the settlement rate in cm/s. Equating tothe buoyant weight of a spherical soil grain gives

6�r�v ¼4

3�r3ð� � �wÞg ð7:2Þ

where � and �w are respectively the density of the soil grain and that of water, andg is the acceleration of gravity. Solving for velocity v gives

v ¼2ð� � �wÞgr2

9�ð7:3Þ

Thus, the settlement rate v depends on the square of the particle radius r.

Experiments have confirmed the validity of the formula for particles between0.001 and 0.10mm in size, that is, for silt and most clay particles. Sand sizes areinfluenced by mass displacement considerations that slow their rates of sinking,

Hydrometer reading, g/l Depth, mm Table 7.2

Depth to hydrometer

center of volume5 155

10 147

15 138

20 130

25 122

30 114

35 106

40 97

45 89

50 81

Note: Adapted from ASTM Designation D-422.




and sizes smaller than about 0.001mm settle more slowly. In 1827 an Englishbotanist, Robert Brown, noticed that pollen grains suspended in water jiggledabout when observed in a microscope, a movement that now is called Brownianmotion. This grabbed the attention of an employee of the Swiss patent office, whowrote a brief paper attributing it to random molecular bombardment. Theemployee’s name was Albert Einstein, who later became famous for anothermatter. Particles smaller than about 0.001mm tend to remain in suspension andare referred to as colloidal size particles.

According to eq. (7.3) the rate of settling depends on the specific gravity � of theparticles, which varies depending on the mineral. Because sedimentation is a bulktest, an average specific gravity is used in the calculations for particle size.A method for measuring average specific gravity is described later in this chapter.However, the assumption that all grain densities are average means that particlesof dense minerals will be reported as larger than their true dimensions becausethey settle faster.

Sedimentation rate is influenced by the fluid viscosity, �, which in turn depends ontemperature. A standardized temperature of 208C (688F) is used for laboratoryanalyses. Other temperatures may be used with appropriate correction factorsbased on viscosity tables.

An obvious limitation of Stokes’ Law is that it applies only to spherical particles,whereas silt grains are angular and clay particles flat. Particle sizes determinedfrom sedimentation rates often are reported in terms of ‘‘equivalent particlediameters.’’

7.4.5 Simplifying Stokes’ Law

In eq. (7.3), a particle radius in cm equals the diameter 0.05D inmm. The settlingvelocity in cm/s equals 600L/T, where L is the settling distance in mm and T istime in minutes. Substituting values for the acceleration of gravity and theviscosity gives

D ¼ Kffiffiffiffiffiffiffiffiffiffiffiffiffiffi

L=10Tp

ð7:4Þ

where D and L are in mm and T is in minutes. K depends on the specific gravity ofthe soil and temperature of the solution; with a representative soil specific gravityof 2.70, and a standardized temperature of 208C, K¼ 0.01344. Other values forthis coefficient for different specific gravities and temperatures are given in ASTMDesignation D-422.

Example 7.3A soil suspension is prepared containing 50 g/l. After 60 minutes the hydrometer reads22 g/l. The temperature is controlled at 208C. (a) What particle diameter is being measured,

and (b) what is the percent of particles finer than that diameter?




Answer: (a) The effective depth of the hydrometer is obtained by interpolation of data inTable 7.2, which gives L¼ 127mm. From eq. (7.4),

D ¼ 0:01344ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

127=10� 60p

¼ 0:0062 mm ¼ 6:2mm:

(b) P¼ 100� 22/50¼ 44%.

7.4.6 Interpolating the Percent 2 mm Clay fromHydrometer Analyses

The sedimentation time for a hydrometer analysis to measure 2 mm clay isapproximately 8 hours, which is inconvenient with an 8-hour working day.However, as this part of the accumulation curve often is approximately linearon a semilogarithmic plot, the percent 2mm clay can be estimated from aproportionality of the respective logarithms. As an approximation,

P002 ¼ 0:4P001 þ 0:6P005 ð7:5Þ

7.5 USES OF PARTICLE SIZE DATA

7.5.1 Median Grain Size

As previously mentioned, the size that defines 50 percent of the soil as beingfiner and 50 percent coarser is the median grain size, designated as D50, and isread from the intersection of the particle size distribution curve with the 50percent line, as shown in Fig. 7.3. The median approximates but is not the sameas a mean or average particle size, which would be very difficult to determinebecause it would involve measuring many individual particles and calculating anaverage.

7.5.2 Effective Size and Uniformity Coefficient

A measurement that often is made for sand is the effective size, D10, or the sizewhereby 10 percent of the particles are finer, and was shown by an engineer,Allen Hazen, to correlate with the permeability of filter sands. Hazen defined theuniformity coefficient, Cu, as the ratio D60/D10. The uniformity coefficient canbe as low as 1.5 to 2 for washed sands that are nearly all one size. For engineer-ing uses a soil is said to be ‘‘well graded’’ if it contains a wide range of particlesizes. A well-graded sand-gravel mixture may have a uniformity coefficient of200–300.

Example 7.4The sand in Fig. 7.2 has approximate values of D10¼ 0.12mm and D60¼ 0.20mm, from

which Cu¼ 1.7. For engineering purposes this soil would be described as ‘‘poorly graded.’’

Because D10 is off the chart for fine-grained soils, another measure for degree ofuniformity suggested by a geologist, Trask, is the ‘‘sorting coefficient,’’ So, which




is defined as (D75/D25)1/2. A more complicated calculation also may be made to

obtain a statistical standard deviation.

7.5.3 Example of Mechanical Analysis

Measurement of soil particle sizes is called a ‘‘mechanical analysis.’’ Data from amechanical analysis are shown in Table 7.3.

The percent 0.002mm clay is estimated from eq. (7.4), which givesD002¼ 0.4� 8þ 0.6� 21¼ 16 percent finer than 0.002mm. The various sizegrades are as follows:

Size grade Calculated percent by weight

Gravel (retained on No. 10 sieve) 4

Sand (retained on No. 200 minus % gravel) (100 – 65) – 4¼ 31

Silt (coarser than 0.002 mm minus % gravel and sand) (100 – 16) – 4 – 31¼ 49

Clay (finer than 0.002 mm) 16

Colloidal clay (finer than 0.001 mm) (8)

Total100

7.5.4 Granular vs. Fine-Grained Soils

Concrete mixes are designed based on a concept that largest particles aretouching, and progressively finer particles fill in the voids. The same conceptapplies to soils, and a broad range of particle sizes is considered to be ‘‘well

Table 7.3

Mechanical analysis

data and

determinations of

weight percents finer

than sizes indicated

Sieve number

(particle diameter in mm)

Weight percent retained

on each sieve

Weight percent finer

Sieve analysis:

No. 4 (4.76) 0 100

No. 10 (2.0) 4 100 – 4¼ 96

No. 20 (0.84) 4 96 – 4¼ 92

No. 40 (0.42) 3 92 – 3¼ 89

No. 60 (0.25) 7 89 – 7¼ 82

No. 100 (0.147) 4 82 – 4¼ 78

No. 200 (0.075) 13 78 – 13¼ 65

Sedimentation analysis:

(0.025) Hydrometer reading¼ 52

(0.010) ‘‘ 31

(0.005) ‘‘ 21

(0.001) ‘‘ 8




graded.’’ If coarse grains are in contact and voids between them are filled withsmaller particles, the soil must increase in the volume, or dilate, in order to shear.This adds appreciably to the shearing resistance.

In many soils the silt and clay content are high enough to separate larger soilgrains so that shearing can occur through the silt-clay matrix without dilatancy,which causes a marked reduction in the soil shearing strength. Artificial mixturesof sand plus clay show that this property change occurs at about 25 to 30 percentclay. The two distinct modes of behavior distinguish ‘‘granular soils’’ from‘‘fine-grained soils.’’

7.5.5 Soil Mixtures

In Fig. 7.5 a poorly graded silt soil is combined with a poorly graded sand toobtain a more uniform grading. In this example the mix is 50–50, and theconstruction lines are shown dashed. A better grading could be obtained byreducing the percentage of A and increasing that of B. The effectiveness of animproved grading can be determined with strength tests. Geologists refer to a well-graded soil as being ‘‘poorly sorted,’’ which means the same thing even though theconnotations are different.

Flat portions of a particle size accumulation curve indicate a scarcity of thosesizes, and a soil showing this attribute is said to be ‘‘gap-graded.’’ Gap gradingtends to give lower compacted densities and strength, and higher permeability.

7.5.6 Soil as a Filter

Filters are barriers that can transmit water while retaining soil particles thatotherwise would be carried along in the water. Filter soils usually are sands.A common use of a filter is in the toe drainage area in an earth dam, where control

Figure 7.5

Combining twopoorly graded soilsA and B to obtain amore uniformgrading AþB.




of seepage is important to prevent water from emerging on the earth slope where itmight lead to piping and failure. Geotextile filters generally are more expensivebut are easier to install than are layers of sand, and are less likely to be damagedor compromised during construction.

DesignProtective filters act as a drain while resisting clogging by fine particles. They alsocannot permit a breakthrough, and may be required to provide insulation againstfrost action. The finer sizes of particles in a soil filter tend to control itsperformance. Generally the filter F15 size is compared with the D85 size for thebase soil. (To avoid confusion the filter size is designated with F instead of D.)A conservative and acceptable guide for design is F15/D8555.

An additional requirement for the retention of clay, for example in the core of anearth dam, is that F1550.5mm.

Example 7.5Is the sand in Fig. 7.2 an appropriate filter for an earth dam constructed from the glacial till

in the same figure?

Answer: The sand has F15¼ 0.12mm, and the till has D85¼ 0.4mm. Then 0.12/

0.4¼ 0.355, so the filter should perform adequately. In addition F1550.5mm so there

should be little or no clay penetration.

Question: What if the dam is constructed from the loess in the figure?

7.5.7 Geotextile Filters

The apparent opening size (AOS) of geotextile fabrics is defined as O95, which isthe size for 95 percent of glass beads of a particular size grade to pass throughduring sieving (ASTM Designation D-4751). One criterion in regard to filtrationof soil is that O95/D8552 or 3, where D85 is for the soil.

7.5.8 Grouting

Grouting is pumping of a fluid under pressure into a soil so that it either (a)permeates the soil, referred to as injection grouting, or (b) displaces the soil, calledcompaction grouting. The determination of whether a grout will inject into the soilpores or displace the soil is mainly dependent on the relations between therespective particle sizes.

Injection grouting is a common remedial treatment used to solidify loosefoundation soil and rock underneath buildings, dams, and other structures.Injection grouting also is used to seal leaks under dams or lagoons, to seal off andcontain buried hazardous wastes, and to seal off the groundwater aquifers inpreparation for tunneling.




Compaction grouting is a relatively new procedure that normally is intended tolaterally compact and densify loose soil to reduce settlement under a foundationload.

Regardless of the grouting procedure the maximum grouting pressure is limited bythe overburden pressure of the soil, or lateral planar injections can lift the soil.When this occurs, pumping pressure should decrease while the pumping rateincreases, referred to as the grout ‘‘take.’’

If the lateral stress existing in the soil is lower than the vertical pressure fromoverburden, the pumping pressure at which the ‘‘take’’ occurs is that which causesvertical radial cracking and is used as an approximate measure of lateral stress inthe soil. This is called ‘‘hydraulic fracturing.’’ It was first developed in thepetroleum production industry to increase the flow of oil into oil wells.

Grout MaterialsThe most common grout materials for rocks and soils are aqueous suspensions ofPortland cement and/or fly ash. Sand-cement mortar may be used for groutingrubble that has large voids. Bentonite sometimes is used as a sealing grout, but hasthe disadvantage that it will shrink and crack when it dries out.

The first injection grout was developed by Joosten in Germany and uses chemicalsolutions of sodium silicates and calcium chloride, which react to make insolublecalcium silicate and sodium chloride. Some more recent chemical solutiongrouts have been removed from the market because of potentially toxic effectson groundwater. Emulsions of asphalt in water are sometimes used as grout forsealing cracks and joints in basements.

Soil GroutabilityFor injection grouting the particle size ratio is reversed from that used design-ing filters, D15 for the soil and G85 for the grout. To ensure success, the ratioshould be substantially higher than the corresponding ratio of 5 used forfilters. Tests by the U.S. Army Corps of Engineers suggest that the ratio of soilD15 to cement G85 should be a minimum of 20. G85 for Portland cement typi-cally is about 0.040 to 0.050mm. The smaller figure represents high-early strengthcement, and also is fairly representative of fly ashes. Specially ground cementsmay have G85 of only 0.005mm. Bentonite is composed of montmorilloniteparticles that expand on wetting, with an effective hydrated G85 of about0.030mm.

Example 7.6Can any of the soils of Fig. 7.2 be injection grouted with cement grout?

Answer: The soil with the largest D15 is the sand, with D15¼ 0.12mm. For cement, assume

G85¼ 0.050mm. Then D15/G85¼ 2.4� 20, so this sand cannot be injected with cement




grout. The sand still may be a candidate for compaction grouting or injection grouting withchemical solutions, depending on the properties that are required.

As a general guide:

� Gravel or very coarse sand can be injection grouted with cement and/or flyashs.

� Medium to fine sand can be compaction grouted with cement/fly ash orinjection grouted with sodium silicate or specially ground fine cement.

� Silt can be compaction grouted.

� Clay cannot be grouted, but expansive clay can be stabilized by a diffusionprocess of hydrated lime, which is much slower than the other processes.

Partly because of the difficulty in controlling injection grouting and knowingwhere the grout goes, compaction grouting has become increasingly popular inrecent years.

7.6 DESCRIBING PARTICLE SHAPE

7.6.1 Particle Shape and Engineering Behavior

The shapes of soil grains can influence engineering behavior, as round grainsobviously are more likely to slip and roll than angular fragments that mesh orinterlock together. For this reason crushed rock normally creates a strongersurface of a ‘‘gravel’’ road than do the more rounded particles of gravel. On theother hand gravel, having been through many cycles of pounding against a beachor river bottom, is more likely to be harder and less likely to degrade into dust.

The main effect of angularity is harshness, or the tendency for the soil to dilate orincrease in volume during shearing, a matter that can be quantified with strengthtests.

Grain shapes closely relate to their mineralogy and origin; quartz sand grainsderived from disintegration of granite tend to be round, whereas grains of feldparderived from the same rock are more angular, and grains of mica are flat. Alluvialgravel generally is well rounded, sand less so, and silt not at all. Dune sand notonly shows rounding, but the grain surfaces are etched from repeated impacts.

The measurement of shapes of individual grains can be time-consuming, butmeasurement of grain profiles can be digitized and automated. A chart that can beused to estimate shape, or ‘‘sphericity,’’ is shown in Fig. 7.6. Sphericitytheoretically is the ratio of a grain surface area to that of a sphere, but can beapproximated by dividing the intermediate grain width by its length. As this does




not take into account the shortest grain dimension, it tends to overestimatesphericity of flat particles such as mica.

7.6.2 Special Problems with the Shape of Mica Grains

Especially troublesome, is that mica particles are flat and also are springy, socompacting a soil with a high content of mica is like trying to compact a bucket ofsprings. Although micaceous soils are not common, their behavior is such thatthey are given a special category in some engineering classifications, and the glitteris not gold.

7.7 TEXTURAL CLASSIFICATION OF SOILS

7.7.1 Describing Different Proportions of Sand þ Silt þ Clay

The first step in characterizing grain sizes in a soil is to take the soil apart andassign the component parts to size grades, namely gravel, sand, silt, and clay. Nextlet us describe the products when we put them back together. A naturallyoccurring gravel deposit almost inevitably will contain some sand, and a naturallyoccurring silt deposit almost inevitably will contain some clay, so when does itstop having ‘‘silt’’ for a soil name and start being a ‘‘clay’’?

‘‘Clay’’ therefore can mean either (a) clay mineral, (b) clay size, or (c) a deposit orsoil that is mainly clay but also contains other minerals and grain sizes. Engineerstend to use a term such as ‘‘clay’’ interchangeably for its several meanings, andshould be certain that it is used in a context that ensures that everybody will knowwhat it means.

Figure 7.6

Chart forevaluating theshapes ofindividual soilgrains from theirprofiles, 1.0representing theapproach to asphere.




7.7.2 Soil Textures and Particle Sizes

Soil scientists who do soil mapping in the field originally proposed the term‘‘texture’’ to describe the ‘‘feel’’ of moist soil squeezed with the fingers. A soilmight have a gritty or sandy feel, or it might have a smooth feel, more likemodeling clay. ‘‘Loam’’ came to mean a somewhat loose and crumbly feel that isgreat for agriculture.

Soil textures are quantified by relating them to the percentages of sand, silt, andclay. The various ranges are shown on a triangular ‘‘textural chart’’ such asFig. 7.7. Boundaries on textural charts have been changed from time to time assize definitions have changed, but the concept remains valid and useful.

The textural chart is read by entering any two of the three percentages and movingonto the chart in the directions of the corresponding short lines around the edges.For example, the boundary between clay and clay loam is at 30 percent clay-sizematerial. It will be seen that a clay texture can contains as much as 55 percentsand. However, to qualify as a sand texture the soil must contain over 80 percentsand.

Textural terms apply to the non-gravel portion of a soil, so the percentages areadjusted for gravel content. If the gravel content exceeds 10 percent the soil is‘‘gravelly.’’

Figure 7.7

A soil texturalchart based onthe 0.075 mmdefinition of siltsize andthe 0.002 mmdefinition of claysize.




Example 7.7What is the textural classification for the soil in Section 7.5.3?

Answer: The soil contains 31% sand and 49% silt. These figures are adjusted for the 4%gravel content: 31/0.96¼ 32.6% sand and 49/0.96¼ 51.0% silt. The texturally is ‘‘silty clay

loam.’’

7.8 SPECIFIC GRAVITY OF SOIL PARTICLES

7.8.1 Definition and Use

Specific gravity is defined as the density of a material divided by the density ofwater at 48C, which is water at its densest. According to eq. (7.3) the specificgravity is required in order to interpret settlement analyses. Some representativespecific gravities for different minerals are shown in Table 7.4. Most sands havea specific gravity of 2.65–2.68; most clays, 2.68–2.72.

7.8.2 Measurement

A common method for measuring the specific gravity of a large object is to weighit in air and then submerge it in water. The difference equals the weight of thewater displaced, a discovery made by Archimedes in his search for a way todetermine the purity of gold. The weight divided by the weight lost therefore

Gold 19.3 Terribly expensive Table 7.4

Specific gravities of

some selected solids

Silver 10.5 Pocket change

Galena (PbS) 7.5 Cubes that look like silver but aren’t

Pyrite (FeS2) 5.0 Cubes that look like gold but aren’t

Hematite (Fe2O3) 4.9–5.3 Red iron oxide in soils

Limonite (Fe2O3 �nH2O) 3.4–4.3 Yellow or brown iron oxides in soils

Iron silicate minerals 2.85–3.6 Dark minerals in basalt, granite

Calcite (CaCO3) 2.72 Most abundant mineral in limestone

Micas 2.7–3.1 Flakey

Quartz(SiO2) 2.65 Most abundant mineral in soils

Feldspar (Na and Ca silicates) 2.55–2.65 Most abundant mineral in rocks

Kaolinite 2.61 Clay mineral

Smectites 2.2–2.7 Expansive clay minerals

Glass 2.2–2.5 Lead glass ¼ 3

Halite (NaCl) 2.1–2.3 Rock salt

Liquid water (H2O) 1.00 At its densest, 48C

Ice (H2O) 0.918 Floats on liquid water




represents the weight divided by the weight of an equal volume of water, which bydefinition is the specific gravity:

G ¼W

W �Wbð7:6Þ

where G is the specific gravity and W and Wb are the weight and buoyant weightrespectively.

A slightly different procedure is used for soils and is a bit more tricky. A flaskis filled with water and weighed; call this A. Then W, a weighed amount of soil,is put into the flask and displaces some of the water, giving a new totalweight, C. As shown in Fig. 7.8, the weight of the water displaced is (AþW�C).Hence,

G ¼W

AþW � Cð7:7Þ

Experimental precision is unhappy with subtracting a weight from thedenominator, so measurements are exacting. Recently boiled or evacuateddistilled water ensures that there is no air that might come out of solution tomake bubbles, and clay soils are not previously air-dried. Less critical is atemperature-dependent correction for the specific gravity of water, which at 208Cis 0.99823. (Specific gravities are reported to three significant figures.) Details arein ASTM Designation D-854. It will be noted that weights and not masses aremeasured, even though the data are usually recorded in grams.

Example 7.8A flask filled to a reference mark with water weighs 690.0 g on a laboratory scale. When

90.0 g of soil are added, the filled flask weighs 751.0 g. The water temperature is 208C.(a) What is G? (b) What effect will the temperature correction have? (c) What if as a resultof measurement error the soil weight is 1 g too high, an error of 1.1%?

Fig. 7.8 Using apycnometer tomeasure specificgravity.




Answer:

(a) G¼ 90/(690.0þ 90.0 – 746.0)¼ 2.65.

(b) Dividing by 0.998 to correct for water temperature does not affect theanswer.

(c) G0 ¼ 91/(690þ 91 – 746)¼ 2.53. A suggested assumed value would bemore accurate.

Problems

7.1. Plot a particle size accumulation curve for soil No. 4, Table 7.5, by enter-ing the data on a computer spreadsheet and selecting the logarithmicoption for the particle sizes. (Optionally this can be done manually using5-cycle semilogarithmic paper.) (a) Evaluate the effective size and unifor-mity coefficient. (b) What is the median grain size? (c) Defining clayas 50.002mm, silt as 0.002–0.074mm, sand as 0.074–2.0mm, and gravelas42.0mm, what are the percentages of clay, silt, sand, and gravel?

7.2. Classify soil No. 4 according to the chart in Fig. 7.7 after adjusting thepercentages for gravel content.

7.3. Plot a particle size accumulation curve for soil No. 1, Table 7.5. (a) Identifythe median and mode(s). (b) If there are two modes, what is the approxi-mate percentage of each soil in the mixture? (c) Using the size gradesdefined in Problem 7.1, find the percentages of clay, silt, sand, and gravel.(d) Adjust the grade percentages for gravel and classify the soil by the chartin Fig. 7.7.

7.4. Calculate the effective size and uniformity coefficient for soil No. l.

Answer: D10¼ 0.0039mm, Cu¼ 192.

7.5. By inspection indicate which of the soils in Table 7.5 should be designatedas gravelly.

7.6. For the first five soils in Table 7.5 compare measured 0.002mm claycontents with those interpolated from the 0.001mm and 0.005mm claycontents by eq. (7.5).

7.7. What is meant by a ‘‘well-graded’’ soil? What is the reason for consideringsuch a soil to be well graded?

7.8. Which soils in Table 7.5 can be injection-grouted with a mixture of Portlandcement, fly ash, and water?

7.9. Soil No. 12 in Table 7.5 is to be separated from No. 14 by means of a filter.From the two particle size accumulation curves, define (a) desirablecharacteristics of a geotextile filter, (b) the gradation(s) required for soilfilter(s): if a single filter layer is not adequate, use two. (c) Select appropriatesoil(s) from the table to use as filter(s).




Tab

le7.5

Mechanic

alanaly

sis

of

soils

:perc

enta

ge

passin

gvarious

sie

ve

siz

es

Sie

ve

num

ber

and

siz

eof

openin

g(m

m)

Sedim

enta

tion

siz

e(m

m)

Soil

No.

1in

.

26.7

3 4in

.

18.8

3 8in

.

9.4

No.

4

4.7

5

No.

10

2.0

0

No.

40

0.4

2

No.

60

0.2

5

No.

100

0.1

49

No.

200

0.0

74

0.0

50

0.0

05

0.0

02

0.0

01

LL

PI

Soil

No.

1100

90

80

72

67

56

44

34

24

21

11

74

29

71

2100

99

98

97

96

91

80

71

63

34

25

18

39

14

2

3100

99

96

92

80

73

41

31

23

76

21

3

4100

97

84

66

50

32

24

54

454

16

4

5100

96

85

61

34

31

13

10

769

75

6100

95

88

80

54

25

14

535

10

6

7100

99

98

95

97

680

97

8100

97

76

60

45

35

21

10

35

17

8

9100

95

88

81

65

59

18

11

627

59

10

100

99

97

93

70

58

56

44

42

24

17

11

41

12

10

11

100

98

92

82

50

42

35

28

25

12

85

38

16

11

12

100

93

77

64

48

24

20

16

12

11

87

613

412

13

100

99

84

48

12

8––

––

––

––

N.P

.13

14

100

99

95

93

68

49

34

86

49

14

15

100

79

60

48

34

30

14

11

924

815

16

100

94

89

87

85

81

73

39

24

12

59

43

16

17

100

98

94

48

42

33

26

22

13

11

10

47

24

17

18

100

98

97

96

94

91

90

89

86

80

42

27

16

45

17

18

19

100

45

38

30

22

20

10

74

16

619

20

100

98

96

95

93

89

64

44

29

84

53

20




7.10. Combine soils 1 and 3 in Table 7.5 in such proportions that the resultingmixture contains 20 percent 5 mm clay. Draw the particle size accumulationcurve of the mixture.

References and Further Reading

Grim, Ralph E. (1962). Applied Clay Mineralogy. McGraw-Hill, New York.

Koerner, Robert M. (1990). Designing with Geosythetics, 2nd ed. Prentice-Hall, EnglewoodCliffs, N.J.

Mitchell, J.K. (1993). Fundamentals of Soil Behavior, 2nd ed. John Wiley & Sons,New York.

Sherard, J. L., Dunnigan, L. P., and Talbot, J. R. (1984). (a) ‘‘Basic Properties of Sand andGravel Filters,’’ and (b) ‘‘Filters for Silts and Clays.’’ ASCE J. Geotech. Engr. Div.110(6), 684–718.

Sherard, James L. (1987). ‘‘Lessons from the Teton Dam Failure.’’ Engng. Geol. 24,239–256. Reprinted in G.A. Leonards, ed., Dam Failures, Elsevier, Amsterdam, 1987.




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